Nuprl Lemma : fps-ucont_wf
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[r:CRng]. ∀[G:PowerSeries(X;r) ⟶ PowerSeries(X;r)]. (fps-ucont(X;eq;r;f.G[f]) ∈ ℙ)
Proof
Definitions occuring in Statement :
fps-ucont: fps-ucont(X;eq;r;f.G[f]),
power-series: PowerSeries(X;r),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type,
crng: CRng
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fps-ucont: fps-ucont(X;eq;r;f.G[f]),
so_lambda: λ2x.t[x],
crng: CRng,
rng: Rng,
so_apply: x[s]
Lemmas referenced :
all_wf,
bag_wf,
exists_wf,
power-series_wf,
equal_wf,
rng_car_wf,
fps-coeff_wf,
fps-restrict_wf,
crng_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
setElimination,
rename,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. \mforall{}[G:PowerSeries(X;r) {}\mrightarrow{} PowerSeries(X;r)].
(fps-ucont(X;eq;r;f.G[f]) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-09_57_07
Last ObjectModification:
2015_12_27-PM-04_36_02
Theory : power!series
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